What kind of F-curve can be used for a perpetual elastic effect of clock second hand motion?
It looks like you can do this with the &quot;Cycles&quot; curve modifier instead of the Generator modifier.
I did the exact same thing as you to get the elastic curve, but only added two keyframes, one on frame 0, and one on frame 30 (I tried this at 30fps). For the elastic settings, I used an amplitude of 0.1 and a period of 15 frames (1/2 framerate).
To use the Cycles curve modifier, I set it up with these settings:

Note that &quot;Before&quot; and &quot;After&quot; are set to &quot;Repeat with Offset&quot; instead of the  default &quot;Repeat Motion&quot; so they will keep ticking forward, instead of resetting back to the start position every cycle.
This is what the result looks like:

The rotation decreases so the object rotates clockwise, instead of counter-clockwise.
You don't have to use an elastic curve though if you don't want to. If you add keyframes in between the first and last, they will be included in the animation, allowing you to have a more custom ticking animation, like this:

Lastly, I would be sure to poke around with the Cycles modifier and see what you can do with stuff like the Restrict Frame Range options, so that you can stop the clock, or only use a specific region of frames. (Ex: if you want to animate it rewinding later, so that only the ticking part of the animation is repeated).